en pl
en pl

Decyzje

Show issue
Year 06/2016 
Issue 26

Weighing Evidence In Favour Of Research Hypotheses Using Bayes Factor: Examples Of Application In Empirical Studies

Artur Domurat
Akademia Leona Koźmińskiego

Michał Białek
Akademia Leona Koźmińskiego

06/2016 (26) Decyzje

DOI 10.7206/DEC.1733-0092.79

Abstract

Statistical tests are used in science in order to support research hypotheses (theory, model). The Bayes Factor (BF) is a method that weighs evidence and shows which out of two hypotheses is better supported. Adopting the BF in statistical inference, we can show whether data provided stronger support for the null hypothesis, the alternative hypothesis or whether it is inconclusive and more data needs to be collected to provide more decisive evidence. Such a symmetry in interpretation is an advantage of the Bayes
Factor over classical null hypothesis signifi cance testing (NHST). Using NHST, a researcher draws conclusions indirectly, by rejecting or not rejecting the null hypothesis. The discrepancy between these decisions and the researcher’s needs, often leads to misinterpretation of signifi cance test results, e.g. by concluding that non-signifi cant p-values are evidence for the absence of differences between groups or that variables are independent. In this work we show the main differences between the Bayesian and
the frequential approach to the understanding of probability and statistical inference. We demonstrate how to verify hypotheses using the BF in practice and provide concrete examples of how it modifi es conclusions about empirical fi ndings based on the NHST procedure and the interpretation of p-values. We discuss the advantages of the BF – particularly the validation of a null hypothesis. Additionally, we provide some guidelines on how to do Bayesian statistics using the freeware statistical program JASP 0.8.

References

  1. Aczel, B., Palfi , B., Szaszi, B., Szollosi, A., & Dienes, Z. (2015). Commentary: Unlearning implicit social biases during sleep. Frontiers in Psychology, 6, 1428. [Google Scholar]
  2. Aranowska, E., & Rytel, J. (1997). Istotność statystyczna – co to naprawdę znaczy? Przegląd Psychologiczny, 40, 249-260. [Google Scholar]
  3. Barr, N., Pennycook, G., Stolz, J.A., & Fugelsang, J.A. (2015). The brain in your pocket: Evidence that Smartphones are used to supplant thinking. Computers in Human Behavior, 48, 473-480. [Google Scholar]
  4. Baumeister, R.E., Bratslavsky, E., Muraven, M., & Tice, D.M. (1998). Ego Depletion: Is the Active Self a Limited Resource? Journal of Personality and Social Psychology 74, 1252-1265. [Google Scholar]
  5. Bayes, M., & Price, M. (1763). An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, FRS Communicated by Mr. Price, in a Letter to John Canton, AMFRS. Philosophical Transactions of the Royal Society of London, 53, 370-418. [Google Scholar]
  6. Białek, M., (2015) Przegląd badań współczesnej kognitywistyki nad efektem przekonań. Przegląd Filozofi czny. Nowa seria, 95, 91-107. [Google Scholar]
  7. Carlin, B.P., & L ouis, T.A. (1997). Bayes and empirical Bayes methods for data analysis. Statistics and Computing, 7, 153-154. [Google Scholar]
  8. Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25, 7-29. [Google Scholar]
  9. De Neys, W., & Franssens, S. (2009). Belief inhibition during thinking: Not always winning but at least taking part. Cognition, 113, 45-61. [Google Scholar]
  10. De Neys, W., & Glumicic, T. (2008). Confl ict monitoring in dual process theories of thinking. Cognition, 106, 1284-1299. [Google Scholar]
  11. Dienes, Z. (2011). Bayesian versus orthodox statistics: Which side are you on? Perspectives on Psychological Science, 6, 274-290. [Google Scholar]
  12. Dienes, Z. (2014). Using Bayes to get the most out of non-signifi cant results. Frontiers in Psychology, 5, 781. [Google Scholar]
  13. Dienes, Z. (2016). How Bayes factors change scientifi c practice. Journal of Mathematical Psychology, 72,78–89. [Google Scholar]
  14. Domański, H., & Pruska, K. (2000). Nieklasyczne metody statystyczne. Warszawa: PWE. [Google Scholar]
  15. Domurat, A., Kowalczuk, O., Idzikowska, K., Borzymowska, Z., & Nowak-Przygodzka, M. (2015). Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations. Frontiers in Psychology, 6, 1194. [Google Scholar]
  16. Edwards, W., Lindman, H., & Savage, L.J. (1963). Bayesian statistical inference f or psychological research. Psychological Review, 70, 193-242. [Google Scholar]
  17. Fisher, R.A. (1955). Statistical methods and scientifi c induction. Journal of the Royal Statistical Society. Series B (Methodological), 17, 69-78. [Google Scholar]
  18. Fisher, R.A. (1925/1950). Statistical methods for research workers. Biological monographs and manuals. No. V. (11th ed.). Londyn: Oliver and Boyd. [Google Scholar]
  19. Frederick, S. (2005). Cognitive refl ection and decision making. The Journal of Economic Perspectives, 19, 25-42. [Google Scholar]
  20. Gaifman, H., & Snir, M. (1982). Probabilities over rich languages, testing and randomness. Journal of Symbolic Logic, 47, 495-548. [Google Scholar]
  21. Gigerenzer, G. (2004). Mindless statistics. The Journal of Socio-Economics, 33, 587-606. [Google Scholar]
  22. Gigerenzer G., Krauss S., Vitouch O. (2004). The null ritual. What you always wanted to know about signifi cance testing but were afraid to ask. W: Kaplan D. (red.), The Sage Handbook of Quantitative Methodology for the Social Sciences (s. 391–408). Thousand Oaks, CA: Sage [Google Scholar]
  23. Haller, H., & Krauss, S. (2002). Misinterpretations of signifi cance: A problem students share with their teachers. Methods of Psychological Research, 7, 1-20. [Google Scholar]
  24. Hays, W.L. (1973). Statistics for the Social Sciences. 2nd ed. Nowy Jork: Holt Rinehart & Winston. [Google Scholar]
  25. Head, M.L., Holman, L., Lanfear, R., Kahn, A.T., & Jennions, M.D. (2015). The extent and consequences of p-hacking in science. PLoS Biology, 13, e1002106. [Google Scholar]
  26. Hu, X., Antony, J.W., Creery, J.D., Vargas, I.M., Bodenhausen, G.V., & Paller, K.A. (2015). Unlearning implicit social biases during sleep. Science, 348, 1013-1015. [Google Scholar]
  27. Jarmakowska-Kostrzanowska (2016). W statystycznym matriksie: kontrowersje wokół testowania istotności hipotezy zerowej oraz p-wartości. Psychologia Społeczna. [Google Scholar]
  28. Jeffreys, H. (1939/1961). Theory of Probability. Oxford: Oxford University Press. [Google Scholar]
  29. Jóźwiak, J., & Podgórski, J. (2001) Statystyka od podstaw. Wyd. V zm. Warszawa: PWE. [Google Scholar]
  30. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454. [Google Scholar]
  31. Kass, R.E., & Raftery, A.E. (1995). Bayes Factors. Journal of the American Statistical Association, 90, 773-795. [Google Scholar]
  32. Koronacki, J., & Mielniczuk, J. (2001). Statystyka dla studentów kierunków technicznych i przyrodniczych. Warszawa: Wyd. Naukowo-Techniczne. [Google Scholar]
  33. Krämer, W., & Gigerenzer, G. (2005). How to Confuse with Statistics or: The Use and Misuse of Conditional Probabilities. Statistical Science, 20, 223-230. [Google Scholar]
  34. Lehmann, E.L. (2011). Fisher, Neyman, and the Creation of Classical St atistics. Nowy Jork: Springer Science & Business Media. [Google Scholar]
  35. Morey, R.D., Romeijn, J.W., & Rouder, J.N. (2016). The philosophy of Bayes factors and the quantifi cation of statistical evidence. Journal of Mathematical Psychology, 72, 6-18. [Google Scholar]
  36. Neyman, J. (1957). “Inductive Behavior” as a basic concept of philosophy of science. Review of the International Statistical Institute, 25, 7-22. [Google Scholar]
  37. Neyman, J., & Pearson, E.S. (1933). On the problem of the most effi cient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, 231, 289-337. [Google Scholar]
  38. Nickerson, R.S. (2000). Null hypothesis signifi cance testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301. [Google Scholar]
  39. Oakes, M. (1986). Statistical inference: A commentary for the social and behavioral sciences. Chichester: Wiley. [Google Scholar]
  40. Pawłowski Z. (1976). Statystyka matematyczna. Warszawa: PWN. [Google Scholar]
  41. Ramsey, F.P. (1931). Truth and probability. W: Trench P.K. (red.), The foundations of mathematics and other logical essays. Londyn: Truber. [Google Scholar]
  42. Stanovich, K. E. (2009). Rational and irrational thought: The thinking that IQ tests miss. Scientifi c American Mind, 20, 34-39. [Google Scholar]
  43. Toplak, M.V., West, R.F., & Stanovich, K.E. (2011). The cognitive refl ection test as a predictor of performance on heuristics-and-biases tasks. Memory & Cognition, 39, 1275–1289. [Google Scholar]
  44. Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110. [Google Scholar]
  45. Tyszka, T. (1999). Psychologiczne pułapki oceniania i podejmowania decyzji. Gdańsk: GWP. [Google Scholar]
  46. Tyszka, T. (2001). Kłopoty z myśleniem probabilistycznym. Roczniki Psychologiczne, 4, 179-191. [Google Scholar]
  47. Tyszka, T. (2010). Decyzje. Perspektywa psychologiczna i ekonomiczna. Warszawa: Wydawnictwo Naukowe SCHOLAR. [Google Scholar]
  48. Tyszka, T., Cieślik, J., Domurat, A., & Macko, A. (2011). Motivation, self-effi cacy, and risk attitudes among entrepreneurs during transition to a market economy. The Journal of Socio-Economics, 40, 124-131. [Google Scholar]
  49. Tyszka, T., Markiewicz, Ł., Kubińska, E., Gawryluk, K., & Zielonka, P. (2016). A belief in trend reversal requires access to cognitive resources. Journal of Cognitive Psychology. [Google Scholar]
  50. Vallverdú, J. (2015). Bayesians Versus Frequentists: A Philosophical Debate on Statistical Reasoning. Nowy Jork: Springer. [Google Scholar]
  51. Villejoubert, G., & Mandel, D.R. (2002). The inverse fallacy: An account of deviations from Bayes theorem and the additivity principle. Memory & Cognition, 30, 171-178. [Google Scholar]
  52. Wagenmakers, E.-J., Morey, R.D., & Lee, M.D. (2016). Bayesian benefi ts for the pragmatic researcher. Current Directions in Psychological Science, 25, 169-176. [Google Scholar]
  53. Wagenmakers, E.J. (2007). A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review, 14, 779-804. [Google Scholar]
  54. Westover, M.B., Westover, K.D., & Bianchi, M.T. (2011). Signifi cance testing as perverse probabilistic reasoning. BMC Medicine, 9, 9-20. [Google Scholar]
  55. Wetzels, R., Matzke, D., Lee, M.D., Rouder, J.N., Iverson, G.J., & Wagenmakers, E.J. (2011). Statistical evidence in experimental psychology an empirical comparison using 855 t tests. Perspectives on Psychological Science, 6, 291-298. [Google Scholar]

Full metadata record

Cite this record

APA style

Weighing Evidence In Favour Of Research Hypotheses Using Bayes Factor: Examples Of Application In Empirical Studies. (2016). Weighing Evidence In Favour Of Research Hypotheses Using Bayes Factor: Examples Of Application In Empirical Studies. Decyzje, (26), 109-141. https://doi.org/10.7206/DEC.1733-0092.79 (Original work published 06/2016AD)

MLA style

“Weighing Evidence In Favour Of Research Hypotheses Using Bayes Factor: Examples Of Application In Empirical Studies”. 06/2016AD. Decyzje, no. 26, 2016, pp. 109-141.

Chicago style

“Weighing Evidence In Favour Of Research Hypotheses Using Bayes Factor: Examples Of Application In Empirical Studies”. Decyzje, Decyzje, no. 26 (2016): 109-141. doi:10.7206/DEC.1733-0092.79.